The effects of external electric field: creating non-zero first hyperpolarizability for centrosymmetric benzene and strongly enhancing first hyperpolarizability for non-centrosymmetric edge-modified graphene ribbon H2N-(3,3)ZGNR-NO2.

How to generate a non-zero first hyperpolarizability for a centrosymmetric molecule is a challenging question. In this paper, an external (pump) electric field is used to make a centrosymmetric benzene molecule generate a non-zero value of the electric field induced first hyperpolarizability (β (F) ). This comes from the centrosymmetry breaking of electron cloud. Two interesting rules are exhibited. (1) β (F) is anisotropic for different directional fields (F i, i = X, Y, Z). (2) The field dependence of β (F) is a non-monotonic function, and an optimum external electric field causes the maximum value of β (F) . The largest first hyperpolarizability β (F) reaches the considerable level of 3.9 × 10(5) a.u. under F Y = 330 × 10(-4) a.u. for benzene. The external electric field effects on non-centrosymmetric edge-modified graphene ribbon H2N-(3,3)ZGNR-NO2 was also studied in this work. The first hyperpolarizability reaches as much as 2.1 × 10(7) a.u. under F X = 600 × 10(-4) a.u. for H2N-(3,3)ZGNR-NO2. We show that the external electric field can not only create a non-zero first hyperpolarizability for centrosymmetric molecule, but also remarkably enhance the first hyperpolarizability for a non-centrosymmetric molecule.